- Option : A
- Explanation : Number of ways in which 8 balls can be drawn

out of 15 is^{15}C_{8}

Number of ways of drawing 2 red balls is^{5}C_{2}

and corresponding to each of these^{5}C_{2}ways

of drawing a red ball, there are^{IO}C_{5}ways of

drawing 6 black balls.

Hence total number of ways in which 2 red

and 6 black balls can be drawn = 5C_{2}X 10C_{6}Required Probability =

= 140/429

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- Option : A
- Explanation : A can draw a ticket in
^{3}C_{1 }= 3 ways.

Number of cases in which A can get a prize

is clearly 1.Probability of A's success = 1/3

Again B can draw a ticket in

Number of ways in which B gets all blanks

Number of ways of getting a prize

= 84 - 20 = 64Thus, probability of B's success =

A's probability of success : B's probability

of success

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14. The chance that a leap year selected at random will contain 53 Sundays is

- Option : B
- Explanation : A leap year consists of 366 days, so that there

are 52 full weeks (and hence 52 Sundays) and

two extra days. These two days can be

(i) Monday, Tuesday

(ii) Tuesday, Wednesday,

(iii) Wednesday, Thursday

(iv) Thursday, Friday

(v) Friday, Saturday

(vi) Saturday, Sunday

(vii) Sunday, Monday

Of these 7 cases. the last two are favourableRequired probability = 2/7

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15. P(A ∩ B'/C) + P(A ∩ B/C) = P(A/C)

- Option : A
- Explanation :

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